Quantitative Bias Analysis Under the Marginal Structural Modelling Framework

OBJECTIVES: Quantitative Bias Analysis (QBA) is a set of methods to study different biases. It is particularly well-suited to quantifying the impact of missing data and unmeasured confounders on study results. Our primary objective is to assess the performance of the delta-adjustment and confounder functions (c-functions), two QBA methods, under the marginal structural modelling (MSM) framework via a simulation study.

METHODS: QBA was performed in presence of three missing mechanisms: missing completely at random (MCAR); missing at random (MAR); and missing not at random (MNAR). We first measured the impact of missingness after performing multiple imputation. Then, we assessed how delta-adjustment and c-functions aid in conducting sensitivity analyses. We also measured if the standardized means differences (SMDs) are useful to assess if sensitivity analyses are needed.

RESULTS: The utility of delta-adjustment following multiple imputation is debatable. Indeed, our simulation study showed that multiple imputation is quite robust, even under the MNAR scenario. In contrast, biases were substantial when a time-varying confounder was omitted. In this context, c-functions were effective at reducing bias from unobserved confounders. In practice, SMDs are used as key indicators for verifying covariate balance and determining the necessity of further investigations. However, in our findings, SMDs did not always accurately indicate the need for sensitivity analyses, even when the treatment effect was heavily biased.

CONCLUSIONS: Although valuable and recommended by regulatory bodies, QBA is infrequently used, and few methods exist for time-varying settings. More advanced QBA methods, such as the c-functions, should be included in routine practice. The decision to employ QBA should not depend solely on metrics like SMDs but should also consider expert opinion and literature findings.